In this paper, radiation patter, as of a thin circular conducting loop embedded in a two-layered spherical chiral medium but illuminated by a plane wave are obtained. The method of moments is employed in this work to formulate the current distribution along the circular loop enclosed by the spherical chiral radome shell. The dyadic Green's functions defining electromagnetic fields due to sources in both the outer and inner regions are applied. In the Galerkin's procedure for the method of moments, basis functions used in the work are sine and cosine functions which form a Fourier series. The formulation itself here is quite compact, straightforward, and easy-to-use. Effects of various geometrical and dielectric parameters of the chiral radome shell are discussed. As expected, the role of the spherical chiral radome is again realized as a polarization transformer. Associated with these parameters, waves and fields in such an electromagnetic system are characterized. It should pointed that there existed some mistakes in the literature which did not use the correct Green's functions in the method of moments procedure. This paper aims at correcting the mistake and establish a correct concept in the method of moments analysis.